Question

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:

• A. 2592
• B. 2866
• C. 2976
• D. 3140

Hint:

For air-filled solenoids, permeability \( \mu_r = 1 \). Always check the unit consistency when using formulas.

Answer 1

The Correct Option is C

The inductance of a solenoid is given by the formula: \[ L = \mu_0 \mu_r \frac{N^2 A}{l} \] where:
\( L = 0.016 \) H (Inductance),
\( \mu_0 = 4\pi \times 10^{-7} \) H/m (Permeability of free space),
\( \mu_r = 1 \) (for air-filled solenoid),
\( A = \pi r^2 = \pi (0.02)^2 \) m\(^2\),
\( l = 0.81 \) m (Length),
\( N \) is the number of turns. Rearranging for \( N \): \[ N = \sqrt{\frac{L l}{\mu_0 \mu_r A}} \] Substituting values: \[ N = \sqrt{\frac{(0.016) (0.81)}{(4\pi \times 10^{-7}) (1) (\pi (0.02)^2)}} \] Solving this gives: \[ N \approx 2976 \] Thus, the correct answer is (3).